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CPK as a DOE response

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  • #30570

    Miguel Camargo
    Participant

    Hi all,
    I am working on a project for improving the CPK on certain process. In other hand, the data results are not normal, so that we need to transform the results as a way for achieving normality.
    Would be OK to use the CPK as a response? If it won’t, What parameter would be better to use as a response (sdev, mean, median, etc)?
    Best Regards,
     
     

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    #79723

    Mike Carnell
    Participant

    Miguel,
    You can improve Cpk (Ppk) two ways: move the mean or reduce the std. deviation. Which one are you trying to do?
    If you are running ANOVA as the DOE it is already a test of means. The sample size you run by treatment should be selected based on the amount of shift in the mean you need to show significance.
    Standard deviation can be used as a response and frequently is.
    If your response isn’t normally distributed – which it may not be just because the sample sizes used in ANOVA are small – were they normal going into the DOE?
    Did you do GR&R on your factors and the response. When you crank up the lights on the measurement system during a DOE people can do some really strange stuff. Try remeasuring the response if you can.
    I wouldn’t use Cpk as a response (this is just my opinion) simply because it is a function of location and size of the standard deviation. Anova already will test the means and you can run the standard deviation separatly and you can see which one is doing what. It may also lack enough sensitivity to let you know when something has changed.
    I really don’t have the data to support this but from what you have said it really seems like you are inthe middle of a DOE before you had really run out your options in Analize.
    Good luck.

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    #79733

    michael Chen
    Participant

    Hi Mike:
    Lack enough sensitivity to let you know when something has changed,even your CTQ is Cpk.Here has one sample for your reference:
    For injection molding industry,the customer always care your process capability,Cpk study is required.When the Cpk can’t meet their target,they should  make DoE to find the optimized parameter and reduce variation,the response may be dimension,strengthen or pull force,etc…It’s more directly to find the “vital X” and to last control limited.

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    #79735

    Hemanth
    Participant

    hi
    Dont use Cpk as your response. What is the product/process characteristic you are measuring? Use that as your response. As for improving Cpk, there are two approaches:
    a,. Reduce variation (std devn)
    b. Bring your process closer to target (shift your process mean)
    Always start with reducing variation. and then try to bring your process closer to target.
    Hope this helped.
    Hemanth

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    #79737

    Cone
    Participant

    Miguel,
    Cpk is not an appropriate response for a DOE because it does not meet the assumptions for the analysis (not normal and also highly volitile because it is so dependent on the location of the mean with respect to a limit).
    You should have been taught this in Black Belt training but you don’t have to make a choice of analyzing mean or standard deviation, you should do it every time and it is just the simple addition of analyzing the residuals of your final model. Minitab faciliates this with some simple graphs. Using Standard Deviation as a response is bogus and just plain wrong – you will miss important things.
    The analysis is called a nodified Box Myers analysis if you want detail. It is the simple looking at a few graphs and maybe doing one or two more looks at the residuals based on the graphs in Minitab.

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    #79760

    Mike Carnell
    Participant

    Michael,
    I may have missed the point of your post but I will respond the way I interpreted it.
    We report CTQ’s in terms of Cpk. No argument about that. Cpk is primarily a reporting metric and for the most part a fairly non value add metric. Placing standard deviations into groups/partial groups of 3 standard deviations doesn’t really make anything any clearer.
    The original question was should it be used as a response in a DOE. The answer in my opinion is no.
    Good luck.

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    #79765

    Sambuddha
    Member

    Miguel:
    Cpk is a derived metric (from sd. & specs.). Nothing great/special about that. Except you already know that (as Mike Carnell has pointed out ), there are 2 ways of improving it.
    Thus mean and std. deviation measures will tell you which direction your improvement activity should be aimed. Now Minitab has a response optimizer tool that lets you find set-points in an interactive manner, so that you have the best of both worlds i.e. centered process and minimum variance.
    Stat > DOE > Factorial > Response Optimizer
    But you do this after you have your Gage R&Red, Screening Expt. done (if needed), DOE performed, and you are ready to do optimization.
    So my answer to your question is : use mean and sd. as your responses and optimize your process based on these 2 parameters. That will take care of your Cpk.
    Best,
    Sambuddha
     
    p.s. If you wanted to know about different types of improvement based on methods and scale, here is a pretty informative post by Mike Carnell that you might want to read. It was a different topic; nevertheless it expands on the issue of being a situational user of improvement methodology.

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    #79767

    Carl H
    Participant

    Miguel,
    I agree with earlier posts – First, do Gage R&R and see how much measurement variation is impacting your current Cpk and use this stdev for planning your DOE (# of replicates needed to “see” effects).
    If you are planning on having the ability to see significant effects on stdev from the DOE factors, you will generally need more replicates than are needed to just see effects on the mean of Y. 
    If you did affect stdev in your DOE, you should be able to observe this in residuals vs fits graphs.  In MINITAB, you can run a second DOE analysis on just the sdtev  at each treatment condition but this is a little bit of a pain.  The response optimizer and contour plots in MINITAB are pretty good for picking the “optimum” settings for mean. 
    Just as improtant as stdev is how “sensitive” the mean is to small changes in DOE factors.  Look for factor settings which give a desired mean and wont change the mean much if the factors vary a little – like they do in real life.
    I run a simple DOEPRO software from Air Academy Press and it has a decent stdev and Cpk optimizer with it.
    Regards,
    Carl
     

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